- Series
- Probability Working Seminar
- Time
- Tuesday, September 22, 2026 - 3:30pm for 1.5 hours (actually 80 minutes)
- Location
- Skiles 006
- Speaker
- Cheng Mao – Georgia Tech – cheng.mao@math.gatech.edu – https://cmao35.math.gatech.edu
- Organizer
- Benjamin McKenna
(first of two talks; the second is on Sep. 29)
A random geometric graph (RGG) is generated by first sampling $n$ latent points independently and uniformly from the unit sphere in $R^d$, and then connecting each pair of points if their inner product exceeds a threshold. We study the sharp detection threshold---the largest dimension at which the RGG can be statistically distinguished from the Erdős--Rényi graph with the same edge density $p$. This threshold is conjectured to be $d \asymp (n h(p))^3$, where $h(p)$ is the binary entropy function. Previous works proved this conjecture for dense graphs with constant $p$ and, up to polylogarithmic factors, very sparse graphs with constant average degrees. In this series of two talks, I will discuss a resolution of this conjecture. This is based on joint work with Hang Du, Nike Sun, Yihong Wu, and Jiaming Xu.